This book reports on the state of a research program that I initiated in 1999. It
connects the practice of proper forcing introduced by Shelah [64] with the study
of various -ideals on Polish spaces from the point of view of abstract analysis,
descriptive set theory, measure theory, etc. It turns out that the connection is far
richer than I dared to imagine in the beginning. Its benefits include theorems about
methodology of forcing as well as isolation of new concepts in measure theory
or abstract analysis. It is my sincere hope that this presentation will help to draw
attention from experts from these fields and to bring set theory and forcing closer
to the more traditional parts of mathematics.